Theorem simp3i 1139

Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)

Hypothesis

Ref	Expression
3simp1i.1	⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)

Assertion

Ref	Expression
simp3i	⊢ 𝜒

Proof of Theorem simp3i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)
2		simp3 1136	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
3	1, 2	ax-mp 5	1 ⊢ 𝜒

Syntax hints:   ∧ w3a 1085

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 396  df-3an 1087

This theorem is referenced by:  hartogslem2  9232  harwdom  9280  divalglem6  16035  structfn  16785  strleun  16786  oppchomfval  17340  sratset  20365  srads  20368  tngip  23715  dfrelog  25626  log2ub  26004  birthdaylem3  26008  birthday  26009  divsqrtsum2  26037  harmonicbnd2  26059  lgslem4  26353  lgscllem  26357  lgsdir2lem2  26379  lgsdir2lem3  26380  mulog2sumlem1  26587  siilem2  29115  h2hva  29237  h2hsm  29238  h2hnm  29239  elunop2  30276  wallispilem3  43498  wallispilem4  43499  prstchomval  46241